In General

•We have a model and data

•Goal: estimate parameter(s) of the model

•The likelihood method is a general method

that solves this problem.

•Likelihood inference has very good theoretical

properties. Those will be covered in Stat330

and Stat 450.

Likelihood function

•The likelihood is the probability that you observe

the data for specific parameter values

Where

– is the set of all possible parameter values

–D are random variables

–And d are realizations from those random variables

( ) Pr( ; ) LDd

Likelihood Method: in search of

parameter values

1. Define the likelihood function L()

–

2. Find the value for the parameter that

maximizes L()

–In practice we always maximize the log likelihood

3. The value that maximizes the likelihood, the

estimate of , is called the maximum

likelihood estimate

– for the Gaussian model

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